An ion cyclotron uses a magnetic field to deflect an ion moving at some velocity through the field. For a spatially uniform magnetic field having a flux density B, a moving ion of mass m and charge q will be bent into a circular path in a plane perpendicular to the magnetic field at an angular frequency .omega..sub.0 in accordance with .omega..sub.0 =qB/m. Thus, if the magnetic field strength is known, by measuring the ion cyclotron frequency, it is possible in principal to determine the ionic mass-to-charge ratio m/q. In effect, the static magnetic field converts ionic mass into a frequency analog. Because the cyclotron frequencies for singly charged ions (12.ltoreq.m/q 5000) in a magnetic field of about 3 Tesla span a radio frequency range (10 KHz .ltoreq.f.ltoreq.4 MHz) within which frequency can be measured with high precision, the ion cyclotron is potentially capable of offering extremely high mass resolution and accuracy.
Fourier transform techniques have been utilized in the detection scheme of ion resonance in mass spectrometry. In such techniques, the whole spectrum of ions is excited at once and the whole spectrum is thereafter detected at once. Such Fourier transform ion cyclotron resonance spectroscopy techniques are described further in U.S. Pat. No. 3,937,955 to Comisarow, et al., the disclosure of which is incorporated herein by reference. Fourier transform mass spectrometry excitation and detection techniques are also discussed in the patents to Marshall, et al., U.S. Pat. No. 4,761,545, Goodman, et al., U.S. Pat. No. 4,945,234 and Liang, U.S. Pat. No. 5,248,882.
Fourier transform mass spectrometry has become a powerful analytical tool because of several important advantages as compared with other types of mass spectrometry (MS). For example, Fourier transform MS offers both high resolving power and high mass accuracy. Additionally, because the ions are confined to a cell, multiple MS experiments (MS/MS, MS/MS/MS, etc.) are easy to perform. Chemical reactions involving trapped ions and neutrals can also be studied. Because the reaction times can be varied easily, kinetic and thermodynamic properties can be measured. For these experiments and many others, it is desirable to be able to determine the relative ion abundances accurately.
In any Fourier transform MS experiment, ions are ultimately detected following excitation of ions to a sufficient orbital radius. When the excitation pulse is turned off, the ions continue to orbit at the respective ion frequencies. After a short delay time, the signal induced in detection plates is measured. The intensity of the induced signal is proportional to the number of ions orbiting in the cell, so it can be expected that one could quantitate ion abundance by correlation with the signal intensity. However, during the delay between excitation and detection, the ions undergo collisions with neutral species in the cell. These collisions cause the orbiting ions to lose energy, resulting in a gradual decrease in the orbital radius. Because the induced signal on the detection plates is greater the closer the ions approach the detection plates, this decaying radius results in a gradual decrease in signal intensity. A stylized sequence for an MS experiment to illustrate this process is shown in FIG. 1, illustrating the relative timing of the ionization phase, the excitation phase, and the detection phase, with an idealized observed signal shown schematically in FIG. 2. The idealized time domain signal in FIG. 2, representing the signal on the detection plates corresponding to a well defined ion (or group of ions) orbiting at a constant frequency, is seen to have a magnitude envelope that declines exponentially after the cessation of the excitation phase at t.sub.o (at time=0.000 in FIG. 2).
The signal decay, as illustrated in FIG. 2, has a detrimental effect on the reliability of quantitation of ion species in Fourier transform MS. One way to address this problem is to minimize the number of collisions that orbiting ions are subjected to. This can be accomplished by lowering the pressure in the cell, although for some experiments, high pressures are necessary, as in MS/MS. One means of achieving low pressures during the detection phase, even when higher pressures are required or unavoidable during some part of the experiment, is the use of a differentially pumped dual cell.
In addition to the effect on absolute ion abundance measurements, the decay rates of the signals from different ions can be different, which affects the relative ion abundance measurements. It is desirable to be able to correct for these differential decay rates to obtain accurate relative ion abundance measurements.
One relatively straight-forward way to obtain this correction is by utilizing segmented Fourier transforms. See, e.g., L. J. de Konig, et al., Int. J. Mass Spectrom. Ion Processes, Vol. 95, 1989, pp. 71-92. In such a technique, a transient signal is divided into a number of smaller contiguous segments, and normal Fourier transform processing is performed on the segments. For example, if a transient contains 65,536 (64 K) points, it could be divided into eight segments, each containing 8,192 (8 K) points. Then, the peak heights of the ions in the mass spectra can be plotted as a function of segment, or equivalently, as a function of time (to the resolution of the time period of each segment) within the transient. It is found with such techniques that the signal from each ion species decays exponentially, so that an exponential decay curve can be fitted to the measured signal resulting from any given measured ion. Then, with the fitted parameters for the exponential decay known, and with knowledge of when the excitation phase ended relative to the beginning of detection of the signal, it is possible to extrapolate back in time, using the fitted exponential decay parameters, and thus estimate the abundance of each ion at the time of the end of excitation. The accuracy of such a technique is limited, in part, by the fact that only a limited number of segments are analyzed.
Another approach is described in the United States patent to Farrar, et al., U.S. Pat. No. 5,047,636. In this approach, the digital samples of the time domain signal are transformed into frequency domain data by linear prediction using a linear least-squares procedure. The resulting frequency domain data is then used to determine the mass of the different types of ions present and the relative number of each type of ion.